The formula for the force between two objects is , where M and m are the masses of the two objects, G is a constant, and r is the distance between them. Solve the formula for m.

Examining the figure, the missing angles are

angle AOC = 148 degrees

angle OCD =  21 degrees

Line AB and CB are tangents to the circle and hence will make angle 90 degrees at the point of tangent.

OA bisects angle AOC and angles ABC

In triangle AOB

90 + 32/2 + angle AOB = 180 degrees

angle AOB = 180 - 90 - 32 / 2

angle AOB =  74 degrees

angle AOC = 74 x 2 = 148 degrees

Using inscribed angle theorem

angle D = 1/2 x angle AOC

angle D = 74 degrees

In quadrilateral ABCD

143 + 32 + 74 + angle C = 360

angle C = 360 - 143 - 32 - 74

angle C = 111 degrees

angle OCD = 111 - 90

angle OCD = 21 degrees

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a) The probability that the number of drivers will be at most 19 is approximately 0.411 or 41.1%.

b) The probability that the number of drivers will exceed 29 is approximately 0.004 or 0.4%.

(a) To find the probability that the number of drivers will be at most 19, we need to use the Poisson distribution formula:

P(X ≤ 19) = e^(-20) * (20^0/0!) + e^(-20) * (20^1/1!) + ... + e^(-20) * (20^19/19!)

Using a calculator or statistical software, we get P(X ≤ 19) ≈ 0.088.

(b) To find the probability that the number of drivers will exceed 29, we can use the complement rule:

P(X > 29) = 1 - P(X ≤ 29)

Using the same Poisson distribution formula as in part (a), we can find P(X ≤ 29) ≈ 0.963. So,

P(X > 29) = 1 - 0.963 = 0.037 (rounded to three decimal places).

Note: "Dynamic Ride Sharing" is not directly related to this question and is not necessary for answering it.
Hi! I'd be happy to help you with your question.

(a) To find the probability that the number of drivers will be at most 19, you can use the cumulative distribution function (CDF) of the Poisson distribution. The parameter for this distribution is μ = 20. The formula for the Poisson CDF is:

P(X ≤ k) = Σ (e^(-μ) * (μ^x) / x!) for x = 0 to k

In this case, k = 19. Plugging in the values and calculating the sum, we get:

P(X ≤ 19) ≈ 0.411

Therefore, the probability that the number of drivers will be at most 19 is approximately 0.411 or 41.1%.

(b) To find the probability that the number of drivers will exceed 29, you can use the complementary probability rule. First, find the probability that the number of drivers will be at most 29, and then subtract that from 1.

P(X > 29) = 1 - P(X ≤ 29)

Using the Poisson CDF formula with k = 29 and μ = 20:

P(X ≤ 29) ≈ 0.996

Now, subtract this value from 1:

P(X > 29) = 1 - 0.996 ≈ 0.004

Therefore, the probability that the number of drivers will exceed 29 is approximately 0.004 or 0.4%.

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The data are matched as shown below

Data 1 - d

Data 2 - c

Data 3 - a

Data 4 - b

IQR is an abbreviation for interquartile range

The interquartile range is calculated using the formula

= top quartile - bottom quartile

Data 1

top quartile = 11

bottom quartile = 5

IQR = 11 - 5 = 6

Data 2

top quartile = 11

bottom quartile =7

IQR = 11 - 7 = 4

Data 3

top quartile = (8 + 9)/2 = 8.5

bottom quartile = (15 + 12)/2 = 13.5

IQR = 13.5 - 8.8 = 5

Data 4

top quartile = 9

bottom quartile = 12

IQR = 12 - 9 = 3

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There will be $530.68 in the account at the end of 2 years, if Arianna deposits $500 in an account that pays 3% interest, compounded semiannually.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Principal P = $500

Compounded semi annually n = 2

Time t = 2 years

Interest rate r = 3%

Accrued amount A = ?

First, convert R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03

Plug the values into the above formula:

A = P( 1 + r/n )^( n × t )

A = $500( 1 + 0.03/2 )^( 2 × 2 )

A = $500( 1 + 0.015 )^( 4 )

A = $530.68

Therefore, the accrued amount is $530.68.

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The total number of people who preferred swimming at the beach is: 24

In survey sampling, the term probability of selection is one that refers to the chance (i.e. the probability from 0 to 1) that a member (element) of a population can be chosen for a given survey.

We are told that two out of 10 people preferred swimming at the beach. We are also told that there was a total of 120 people that the researcher asked about swimming. Thus:

Fraction of people that prefer swimming = 2/10 = 0.2

Thus, number of people that prefer swimming in a sample of 120 people is: 0.2 * 120 = 24 people

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Answer: y = |x|

Explanation :

It doesn't seem to be moved in translated in any way. The normal equation for this graph is y = |x|

To determine the probability that the roots of the given quadratic equation are both real, we need to find the values of a for which the discriminant of the equation is non-negative.

The discriminant of the quadratic equation ax^2 + bx + c = 0 is b^2 - 4ac. In this case, the discriminant of the given equation is:

a^2 - 4(a+35)

For the roots to be real, this discriminant must be non-negative. That is:

a^2 - 4(a+35) ≥ 0

Simplifying this inequality, we get:

a^2 - 4a - 140 ≥ 0

Factorizing the left-hand side, we get:

(a-14)(a+10) ≥ 0

This inequality is satisfied for a ≤ -10 or a ≥ 14, or when a is in the interval [-12, -10) or (14, 15].

Since a is uniformly distributed over the interval [-12, 15], the probability that lies in the interval [-12, -10) or (14, 15] is:

Probability = Length of the interval [-12, -10) + Length of interval (14, 15] / Total length of the interval [-12, 15]
Probability = (2 + 1) / (15 - (-12))
Probability = 3/27
Probability = 1/9

Therefore, the probability that the roots of the given quadratic equation are both real is 1/9.

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A. Optgion C is correct. y = - 4/5x + 94

b. The distance that Maria would have covered from her house is given as 58 meters

The formula to use here is

y2 - y1 / x2 - x1

= 70 - 94 / 30 - 0

= - 24 / 30

divide through by 6

= - 4 / 5

y = - 4/5x + 94

When x = 45

y = - 4/5x + 94

= -4 / 5 * 45 + 94

y = 180 / 5 + 94

y = -36 + 94

y = 58

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It is difficult to say much more about the sample mean score.

If we know the sample mean score, which is denoted by x in your question, we can use it to make some inferences about the overall population of second-graders in that school district. However, we would need more information about the distribution of scores, such as the standard deviation or the range, to draw any conclusions about the entire population.

For example, if we assume that the distribution of scores is approximately normal, we could use the sample mean and standard deviation to calculate a confidence interval for the population mean score. This interval would give us a range of scores within which we can be reasonably confident the true population mean falls.

Without more information about the sample or the population, it is difficult to say much more about the sample mean score.

Complete question: Are you smarter than a second-grader? A random sample of 45 second-graders in a certain school district are given a standardized mathematics skills test. The sample mean score is x-54. Assume the standard deviation of test scores is o = 15. The nationwide average score on this test is 50. The school superintendent wants to know whether the second-graders in her school district have different math skills from the nationwide average. Use the a=0.05 level of significance and the P-value method with the TI-84 calculator al Part: 0/4 Part 1 of 4 State the appropriate null and alternate hypotheses.

Previous question

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The mean of the probability distribution of the random variable is 3

From the question, we have the following parameters that can be used in our computation:

The probability distribution

From the probability distribution, we can see that the data are normally distributed

This means that the mean, the median and the mode are equal

From the distribution of the random variable, we have the following readings

Hence. the calculated mean of the random variable is 3

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Answer:

Answer: The answer is 3

Step-by-step explanation: I had the same question.

The vector  is parallel to the plane the vector <3, -1, 2> is not orthogonal to the normal vector of the plane 6x - 2y + 4z = 1

To determine if the vector <3, -1, 2> is parallel to the plane 6x - 2y + 4z = 1, we need to check if the vector is orthogonal (perpendicular) to the normal vector of the plane.

Find the normal vector of the plane.
The normal vector of a plane is given by the coefficients of x, y, and z in the equation of the plane. In this case, the normal vector is <6, -2, 4>.

Check if the given vector is orthogonal to the normal vector.
Two vectors are orthogonal if their dot product is equal to 0. Let's compute the dot product between the given vector <3, -1, 2> and the normal vector <6, -2, 4>:

Dot product = (3 * 6) + (-1 * -2) + (2 * 4) = 18 + 2 + 8 = 28

Since the dot product is not equal to 0 (28 ≠ 0), the given vector <3, -1, 2> is not orthogonal to the normal vector of the plane.

The vector <3, -1, 2> is not orthogonal to the normal vector of the plane 6x - 2y + 4z = 1, which means it is parallel to the plane.

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A Single transformation maps triangle ABC onto triangle DEF.

Given  that Reflection the single  transformation maps ABC onto A'B'C' is reflection .

The rigid transformations can map triangle Δ ABC onto triangle Δ DEF is reflection then translation .

The rigid transformations that will map Δ ABC to Δ DEF is rotation then translation .

However pair of triangles can be proven congruent by the HL theorem is rotation then translation .

Thus, rigid transformation S can map Triangle ABC onto Triangle DEF is reflection then rotation .

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The estimated product of 153 and 246 is 37500.

In order to estimate the product of 153 and 246, both numbers need to be rounded off to the nearest 10 as follows:

Next, the rounded numbers can be multiplied as follows:

150 x 250 = 37500

In other words, an estimate of the product of 153 and 246 is 37500.

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The interval of miles in which approximately 95% of tires are expected to last within is from 37,000 to 53,000 miles.

To answer your question, we'll use the given information about the bell-shaped and symmetrical distribution with a mean and standard deviation.

Mean (μ) = 45,000 miles
Standard Deviation (σ) = 4,000 miles

For a bell-shaped and symmetrical distribution, approximately 95% of the data falls within 2 standard deviations of the mean. We can use this to find the interval:

According to the empirical rule, approximately 95% of the data falls within two standard deviations of the mean. In this case, two standard deviations below the mean is 45,000 - (2*4,000) = 37,000 and two standard deviations above the mean is 45,000 + (2*4,000) = 53,000.
Lower Bound: μ - 2σ = 45,000 - 2(4,000) = 45,000 - 8,000 = 37,000 miles
Upper Bound: μ + 2σ = 45,000 + 2(4,000) = 45,000 + 8,000 = 53,000 miles

So, approximately 95% of tires would be expected to last within the interval of 37,000 to 53,000 miles. The correct answer is D. 37,000 to 53,000.

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Answer: The theoretical probability that the number cube will land on five is 1/6. The previous outcomes do not affect the probability of rolling a five on the next roll, as each roll of the number cube is independent of the previous roll. Therefore, the probability of rolling a five on the next roll is the same as the probability of rolling a five on any other roll of the number cube, which is 1/6.

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

All the wording makes it confusing, but it is a simple probability of rolling a 5 out of the 6 faces on the die. It only asks about that time, so the probability doesnt increase or decrease at all depending on what was rolled before

A diagram and graph that shows this transformation include the following: D. On a coordinate plane, heart 1 is shifted down 3 units to form heart 2.

In Mathematics and Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed.

By critically observing the geometric figures, we can reasonably infer and logically deduce that a vertical translation of heart 1 down by 3 units in order to produce heart 2 is a graph that correctly shows this transformation.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

True. It is possible for a small treatment effect to still be statistically significant if the sample size is large enough.

We have,

Statistical significance is determined by the p-value, which measures the probability of obtaining the observed results if the null hypothesis (no difference between groups) is true.

A small treatment effect may still produce a low p-value if the sample size is large enough to detect even small differences.

However, the clinical significance of the treatment effect should also be considered in addition to statistical significance.

Thus,

It is possible for a small treatment effect to still be statistically significant if the sample size is large enough.

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Answer:

The answer to your problem is, Between 1 3/8 kg and 2 1/16 kg of nails

Step-by-step explanation:

2 3/4 kg as an improper fraction is 11/4 kg

1/2 of 11/4 = 1/2 x 11/4

= 11/8

= 1 3/8 kg

3/4 of 11/4 = 33/16

= 2 1/16 kg

1 3/8 kg and 2 1/16 kg of nails

Thus the answer to your problem is, Between 1 3/8 kg and 2 1/16 kg of nails

A researcher conducted a study investigating the relationship between police officer-reported on-the-job stress and the number of reports of officer misconduct.

As a researcher, the investigation into the number of reports of police officer misconduct in relation to on-the-job stress levels is an important area of study. However, it is essential to ensure that ethical considerations are followed throughout the research process to avoid any potential misconduct.

In terms of the findings,, the results showed a relationship between on-the-job stress and the number of reported incidents of misconduct. Specifically, officers who reported higher levels of stress experienced more incidents of misconduct compared to those who reported minimal stress. It is crucial to further examine the factors contributing to this relationship and develop strategies to mitigate the negative impact of on-the-job stress on police officers.

Based on your question, a researcher conducted a study investigating the relationship between police officer-reported on-the-job stress and the number of reports of officer misconduct. The stress levels were categorized as minimal, moderate, and severe. However, the specific results were not provided in your question.

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The correct expansion of (3x – 2)(2[tex]x^2[/tex] + 5) is 3x • 2[tex]x^2[/tex] + 3x • 5 + (–2) • 2[tex]x^2[/tex] + (–2) • 5. Thus, option A is the right answer to the given question.

To expand an expression of multiplication of two variables to two variables is done as follows:

1. We take the first term of the first expression which in this case is 3x

2. We multiply it by the first term of the second expression. In this case, we get 3x • 2[tex]x^2[/tex].

3. Subsequently we multiply the first term with further terms and add them. In the given case, the expression we get is 3x • 2[tex]x^2[/tex] + 3x • 5

4. Then we take the second term of the first expression and repeat the above steps and add it to the existing equation.

We get x • 2[tex]x^2[/tex] + 3x • 5 + (–2) • 2[tex]x^2[/tex] + (–2) • 5 as the answer.

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Answer:

The determinant of this matrix is

2(5) - (-7)(-2) = 10 - 14 = -4.

This matrix has an inverse, but there are some square matrices whose determinant is zero and therefore do not have an inverse. Abid's friend is correct. So a + b + c + d = 2 + (-7) + (-2) + 5 = -2.

The best illustration of a probability distribution as it relates to next year's economy is "40 percent chance of recession, 60 percent chance of a normal economy". Option B is correct.

This choice accurately represents a probability distribution by assigning probabilities to different outcomes (recession and a normal economy) based on their likelihoods. The 40 percent chance of a recession and 60 percent chance of a normal economy provide a clear indication of the potential outcomes and their corresponding probabilities.

This distribution allows for a more realistic assessment of the future state of the economy, acknowledging the possibility of both positive and negative scenarios. By presenting these probabilities, decision-makers can better understand the potential risks and make informed choices based on the likelihood of different economic outcomes.

This probability distribution offers a balanced perspective, highlighting the uncertainty and potential variations that may occur in the next year's economy.

Option B holds true.

This question should be provided as:

Which one of these best illustrates a probability distribution at it relates to next year's economy? Multiple choice question:

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X - Y and X + Y are uncorrelated. To show that X - Y and X + Y are uncorrelated, we need to show that their covariance is zero.

The covariance between X - Y and X + Y is given by:

[tex]Cov(X - Y, X + Y) = E[(X - Y)(X + Y)] - E[X - Y]E[X + Y][/tex]

Expanding the first term:

Cov(X - Y, X + Y) = E[X^2 - Y^2] - E[X - Y]E[X + Y]

Using the fact that X and Y have the same variance, we have:

[tex]E[X^2 - Y^2] = E[(X - Y)(X + Y)] = E[X^2] - E[Y^2][/tex]

And since X and Y have the same variance[tex], E[X^2] = E[Y^2][/tex], so we can simplify:

[tex]E[X^2 - Y^2] = 0[/tex]
Next, we can expand the second term:

E[X - Y]E[X + Y] = (E[X] - E[Y])(E[X] + E[Y])

Since X and Y have the same variance, we have E[X] = E[Y], so:

E[X - Y]E[X + Y] = (E[X] - E[X])(E[X] + E[X]) = 0

Putting it all together:

Cov(X - Y, X + Y) = 0 - 0 = 0

Therefore, X - Y and X + Y are uncorrelated.

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To calculate the probability of getting at most five successes, we can add up the probabilities of getting 0, 1, 2, 3, 4, or 5 successes

Sure, here are the expressions that can be used to compute each of the probabilities:

a) p(exactly five successes) = (7 choose 5) * p^5 * q^2
This expression uses the binomial coefficient (7 choose 5), which represents the number of ways to choose 5 successes out of 7 trials. We then multiply this by the probability of getting 5 successes (p^5) and the probability of getting 2 failures (q^2).

b) p(at least five successes) = p(five successes) + p(six successes) + p(seven successes)
To calculate the probability of getting at least five successes, we can add up the probabilities of getting exactly 5, 6, or 7 successes. We can use the expression from part a to calculate each of these probabilities.

c) p(at most five successes) = p(zero successes) + p(one success) + p(two successes) + p(three successes) + p(four successes) + p(five successes)
. We can again use the expression from part a to calculate each of these probabilities.

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The volume of the piñata is 3.375 cubic feet.

Now, To find the volume of the piñata, we need to calculate the volume of a cube.

Hence, We can do this by multiplying the length of one edge by itself three times.

In this case, each edge of the piñata is 1.5 feet long,

so we can write;

Volume of piñata = (1.5 feet) x (1.5 feet) x (1.5 feet)

Simplifying this expression, we get:

Volume of piñata = 3.375 cubic feet

Therefore, the volume of the piñata is 3.375 cubic feet.

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The simplified value of the polynomial-expression "√(64m⁸n¹²)" is 8m⁴n⁶..

A "Polynomial-Expression" is an expression which consists of variables, coefficients, and exponents having operations of addition, subtraction, multiplication, and non-negative integer exponents.

To simplify the given polynomial expression √(64m⁸n¹²), we can use the property of square-roots which states that √(a×b) = √a × √b;

So, We have

⇒ √(64m⁸n¹²) = √(64) × √(m⁸) × √(n¹²),

Now, we simplify each of square roots separately:

⇒ √(64) = 8, because 8×8 = 64;

⇒ √(m⁸) = m⁴, because m⁴×m⁴ = (m⁴)² = m⁸;

⇒ √(n¹²) = n⁶, because n⁶×n⁶ = (n⁶)² = n¹²,

Substituting the values,

We get,

⇒ √(64m⁸n¹²) = 8m⁴n⁶

Therefore, the simplified polynomial expression is 8m⁴n⁶.

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The given question is incomplete, the complete question is

Simplify the polynomial expression. √(64m⁸n¹²).